In contrast, a heuristic is a solution method that, like a rule of thumb, can be used to solve a problem but is not guaranteed to do so. For example, some students prepare for a test by using the heuristic of studying class notes while ignoring the reading material. This strategy is neither fool proof nor advisable, yet it does work on some occasions.
The type of strategy that one uses is one' of the chief determinants of problem solving. We often describe problems as being easy or difficult. But the difficulty of problem depends upon the type of strategy used by the problem solver. In turn, whether a particular strategy is appropriate depends upon the capacities and skills of the solver. If a strategy is to be effective; then, it must be tailored to fit the characteristics of both the problem and the solver. Let us examine some of the general strategies that people use keeping the above in mind.
MEANS-ENDS ANALYSIS
Many problems, called problems of transformation, consist of an initial situation, a goal, and a set of operations that can be used to move from the initial situation to the goal. In resolving these problems, people frequently use the heuristic of means-ends analysis. This strategy consists of identifying the principal differences between the initial situation and the goal and then taking actions that reduce those differences. Then this is called a difference-reduction strategy.
This strategy is useful in solving commonplace problems such as how to keep warm outside in winter. In the initial stage you experience the feeling of coldness, and the goal state is the sensation of warmth. The solver (you) takes necessary steps for producing warmth, such as adding clothing, building a fire, or finding shelter from the wind, by using the strategy of means-ends analysis. Of course these actions may also occur in the absence of strategic planning, however people do in many instances strive for goals by using means-ends analysis.
The advantages of the strategy of means-end analysis are illustrated by examining performance on the Tower of Hanoi problem. The initial state of a simple version of this problem is shown in Fig. 30.a. The task is to move the three disks from peg A to pig C in the fewest moves without violating two constrains: move only one disk at a time from the top of a stack and never put a larger disk on top of a smaller disk. The solver succeeds when the disks are arranged on peg C in order one-two-three.
This problem has a clearly definable goal structure in that it can be divided into several sub goals (Egan and Greeno, 1974; Simon, 1979). One sub goal is to move disk three onto peg C. This sub goal is itself divisible into sub goals such as moving disk ( 1) one to peg C, moving disk (2) to peg B, and then moving disk (1) one back to peg B, leaving peg C open to receive disk (3). After moving disk (3) into peg C, the solver then works on the next sub goal of moving disk (2) onto peg C, and so on.
While solving the Tower of Hanoi Problem using the strategy of means-ends analysis, people apparently do formulate and achieve sub goals. For example, Egan and Greeno ( 197 4) observed that the number of errors decreased as the subjects moved closer to the main sub goals of the problem. When the main sub goal being worked on was distant, the solver had to keep track of numerous moves and of how those moves was related to the sub goal. But when the main sub goal ~as only one or two moves away, less planning was required. As a result, the subjects allocated their resources chiefly to the next move; thereby avoiding errors. The view that the subjects had divided the problem. into sub goals was also supported by the results of a recognition test in which the subjects examined various arrangements of disks and stated whether those arrangements had occurred while working on the problem. The results were that they seldom erred in judging arrangements that were inconsistent with the sub goals (for example, an arrangement in which the largest disk was on Peg B). The subjects committed more errors in judging arrangements that were consistent with the sub goals regardless of whether they had actually produced those exact arrangements earlier. This observation suggests that the subjects had indeed formulated sub goals in solving the problem. As we can see, the means-end analysis is only useful because it places light demands on processing capacity. Even that, when the solver formulates sub goals and works on one at time (Simon 1975). Thus means-end analysis confers the benefits of planning while avoiding the excess overlapping of actions.
Means-ends analysis is also useful in solving problems that have no sub goals. But it is sometimes necessary to increase the difference between the current state and the goal state in order to solve a problem. This poses problems for a strict means-ends analysis, which is inherently a difference-reduction strategy.
Means-ends analysis is not always the optimal way to reach a solution, however because sometimes the optimal way involves taking a temporary step, backward or further from the goal. Means-ends analysis can make it more difficult to see that the most efficient path forward a goal isn't always the one that is most direct. Fortunately, people rarely adhere rigidly to only one pure strategy. More often, they work with multiple strategies, adapting their methods to the requirements of the task.
SEARCH STRATEGIES
Searching is a pervasive aspect of problem-solving activities. For example, executing the strategy of means-end analysis involves searching for the optimal procedure for reducing the discrepancy between the current state and the goal state. Similarly, solving an anagram problem, like the problem of forming a legal word from the letters R B E T Y H E, requires searching through various sequences of letters and finding a permissible word. (Solution for this is THEREBY).
More important, searching and planning usually go hand in hand. Searching through the range of options is an essential part of the planning process. A good way to improve your own planning and problem -solving skills is to learn to search explicitly and thoroughly. A search may be conducted in many different ways. It can be searched in either a breadth-.first or a depth-first manner. These search strategies need to be used single-mindedly. In playing. games of strategy, people probably pursue both types of search.
The Generate-Test Strategy
Not all search strategies are as directed and systematic as are breadth -first and depth-first searches. People often use a simple generate-test strategy for searching (Newell and Simon, 19'73 ). This strategy involves generating possible solutions to a problem in a relatively unsystematic manner and testing each candidate to see whether it constitutes a solution. For example, the problems of making a word from the letters NADL can be solved by generating all of the possible combinations of the letters and deciding whether each combination is a word. You probably recognize this as an instance of the generation -recognition strategy that people use to recall lists of items in a free r~call procedure.
The generate -test strategy appears simple, as it boils down to suggesting and testing the first items in a category that come to mind. Unfortunately, this strategy is in many instances insufficient or unworkable, sometimes both. First at all, it involves a relatively undiscriminating search; one simply generates candidates and tests each. This undirected approach works when there are only a few possible solutions to be considered.
But as we know many problems have a large number of possible solutions, too many to be searched efficiently using generate-test procedure. Imagine trying to design an experiment or do a crossword puzzle by generating items in an undirected manner. The possible solutions are so numerous that the actual solution may not be generated in a "reasonable amount of time. The set of all possible solutions that the solver is willing to consider is called the search space. Generally speaking, when the search space is large, the generate-test strategy is inefficient; for the good and the bad candidates for a solution receive equal consideration. What is needed is a way of narrowing the realm of options of reducing the size of the search space-so that only the better candidates receive consideration.
Another limitation of the generate-test strategy is that it involves generating complete candidate solutions. This approach can succeed on well-defined problems such as anagram problems that have readily recognizable solutions. However, this strategy can be useful when there aren't a lot of possibilities to keep track of. If you've lost your keys somewhere between the rear by cafe and your room and you made intermediate stops in a classroom, 1 the snack corner, and the books store, you can use this technique to help you search.
In essence, the generate test method fails to limit the search space to a manageable size. Once again, we need a method for reducing the size of search space so that only the closest approximations to a search solution are considered.
Strategies for Limiting the Search Space
The search space can be kept limited by using variety of memory strategies. One of the simplest involves remembering and searching for only the courses of action that have worked in the past. For instance, if there is a problem, to form a word beginning with the letter Q, you might begin by searching through the list of words beginning with a Q that you had previously seen or produced. This strategy, although not very thoughtful, people often solve such recurring problems by remembering how they solved the problem the last time it was encountered.
There is a more sophisticated memorial strategy consists of reasoning by analogy. In this, we draw a parallel between a poorly understood state of affairs and one we have experienced or studied previously or know more about. This strategy is advantages because it allows us to apply our knowledge of the old state of affairs to the new one, thereby reducing the amount of searching that we have to do in order to solve the current problem. Let us consider an example, the problem of finding a strong and lightweight material that could be used to make an artificial hip. The search space for this problem is potentially very large, so an undirected search would probably take too long and we might never get the appropriate material.
The search space can be reduced if we notice that this problem resembles the problem of constructing an airplane that is sufficiently strong and light enough to fly. Having realized this, scientists can concentrate their search on the materials used to construct airplanes.
Looking at the above example, reasoning by analogy appears to involve the discrimination of similarities in form between two things. Scientists, often use such a strategy in order to bring what is already known to bear on unsolved problems. They sometimes define ill-defined problems by way of analogy with well-defined problems that are better understood. Another type of strategy of limited search space and searching in a highly directed manner is to perform a constructive search (Greeno, 1978). Here, the solver uses his or her semantic and world knowledge to produce a partial solution that reduces the number of options remaining to be searched.
Let us try to solve the by cryptarithmetic problem using constrictive search :
Try to substitute the numbers 0 through 9 for letters in a way that leads to a correct addition. To solve this problem people, usually work on the letters in one column in an attempt to identify the value of particular letter (Newell et al. 1972)
For instance, most people he gin by using their knowledge of a arithmetic to reason that T=O, Since D=5, and 5+5=10. Then the subjects use that partial solution to guide them search. Knowing that the sum of L+L must be an even number but that column two has a carry of 1 (from the addition D +D), the subjects reason that R must be odd. And since, D + G = R, it follows that R must be greater than 5. Continuing in this manner, many subjects solve the problem.
The constructive search strategy is used frequently in attempts to solve everyday problems. For example, typists who must decipher an illegible word may use their knowledge of the context and of the rules of language to determine the probable meaning and grammatical class of the illegible word. Then they undertake a search for semantic memory for words that have the specified properties. In this manner, they avoid the inefficient strategy of generating words at random and testing the appropriateness of each. The constructive search strategy is fundamental in almost all types of investigation. It also leads to the formulation of sub goals. In this respect, it also compliments the heuristic of means-ends, analysis. The benefits of both strategies can be achieved by uniting the two heuristics into a higher-order strategy.
The Confirmation Strategy
Let us now consider how people search for evidence bearing on the validity of hypotheses. This type of search is highly important, to evaluate hypotheses about the mechanical problems of a car, the effectiveness of a particular method of reading etc. In scientific enterprise,''search for evidence has obvious relevance and explains how people search for evidence and collect them.
One of the Chief strategies that people use in evaluating hypotheses has been documented in the following type of tasks (Watson, 1960). The experimenter presented a triad of numbers, 2-4-6, and stated that this triad has been generated by a rule. The subjects' task was to identify the rule by producing some triads of numbers. The experimenter immediately identifies whether they are conforming to or as violating the rule. The subjects were allowed to generate as many triads as they wanted to. They were told to state their hypothesis about the identity of the rule only when they were certain that it was correct. The rule for the above problem was to generate 2-4-6 triad "any three numbers in ascending order'' was used.
Surprisingly, about 0% of the subjects announced incorrect hypotheses in this task, although most of them eventually solved the problem. The poor performance is because they used a confirmation strategy in evaluating their hypothesis. This strategy, which is used in many different tasks (Schustack and Sternberg, 1981) involved searching for evidence that confirmed the hypothesis, but not for the evidence that could have falsified it. In the above problem, one subject formulated the incorrect rule that, she generated triads such as 8-10-12,20-22-24 and 1-3-5, all of which were consistent with the correct rule. She assumed that her hypothesis was correct. The problem is that triads such as 2-4-6 and 1-3-5 can be generated by different rules too. The only way to eliminate
the incorrect rules is to try to falsify them by obtaining disconfirmatory evidence. In order to test her rule of "increasing by twos", the subject described above should have looked for disconfirmatory evidence such as the triad 1-2-3.
Thus, attempts ct falsification are essential in critically evaluating a hypothesis. Though the confirmation strategy is a narrow-minded approach, the positive side of the confirmation strategy should also be recognized. For one thing, the correct hypothesis can sometimes be identified by using the confirmation strategy (Bowers, 1977). Moreover, the use of this strategy makes good sense in the initial stages of inquiry in an area. Additionally it provides valuable clues about when to look in future investigations. Thus, searching for confirmatory evidence can help to guide research.
Ideally, scientists evaluate hypotheses by using the method of strong influence (Platt, 1964), in which they perform experiments designed to simultaneously confirm one hypothesis or class of hypotheses and falsify others. In the advanced stages of research, this method is much more powerful than the confirmation strategy, which fails to isolate the correct hypothesis from other interpretations.
STRATEGIES FOR MAKING PROBABILISTIC INFERENCES
In every day situations, people make many predictions and judgments in the face of uncertainty. We never know before hand with absolute certainty which candidate will be the best national leader or which acquaintance will be the best friend. In such situation~ we must leave certainty and asses the odds, and make a probabilistic prediction or decision. Probabilistic inferences are important in problem solving because people rarely know certainly which strategy will work best. So in selecting a strategy, people are often forced to judge the probability that a particular strategy will succeed.
Probabilistic inferences can be made in several ways. People who have not received any formal training in probability theory (and also some who have) tend to make probabilistic inferences by using the representativeness strategy and the availability strategy (Tversky and Kahneman, 1973; Cohen, 1980).
Representativeness
The representativeness strategy involves judging whether an item is a member of a particular class by evaluating how representative that item is of the class. An item is representative of a class to the extent that it is a typical class member. Thus, representativeness and typicality are closely related concepts and the prototype of a class is the most representative member.
Before you read about representativeness, try the following problem from Kahneman and Tversky (1972).
-~ All the families having exactly six children in a particular city were surveyed. In 72 of the families the exact order of birth of boys and girls was G BG BBG (G= Girl, B=Boy).
What is your estimate of the number of families surveyed in which the exact order of births was BGBBBB?
Most people while judging the number of families with the BGBBBB birth pattern estimated the number to be less than 72. Actually, the best estimate of the number of families with this birth order is 72, the same as for the GBGBBG birth order. The expected number for the second pattern would be the same because the gender for each birth is independent of the gender for every other birth, and for any one birth, the chance of a boy (or a girl) is one out of two. Thus,any particular pattern of births is equally likely (112) 6, even B B B B B B or G G G G G G.
Why do many of us believe some birth orders to be more likely than others? Kahneman and Tversky suggest that it is because we use the heuristic of representativeness, in which we judge the probability of an uncertain event according to
a) How obviously it is similar to or representative of the problem from which it is 1 derivedand
b) The degree to which it reflects the salient features of the process by which it is generated (such as randomness). For example, people believe that the first birth order is more likely because first, it is more representative of the number of females and males in the population, and second, it looks more random than the second birth order. In fact and of course, either birth order is equally likely to occur by chance.
The fact that we frequently rely on the representativeness heuristic may not be terribly surprising because it is easy to use and often it works. According to Tversky and Kahneman ( 1971), another reason that we often use the representativeness heuristic is that we mistakenly believe that small samples (of events, of people, of characteristics, etc.) resemble in all respects the whole population from which the sample is drawn. That is, we particularly tend to underestimate the likelihood from which the sample is drawn. That is, we particularly tend to underestimate the likelihood that the characteristics of a small sample (e. g., the people whom we know well) of a population inadequately represent the characteristics of the whole population.
We also tend to use the representativeness heuristic more frequently when we are highly aware of anecdotal evidence based on a very small sample of the population. Richard Nisbett and Lee Ross ( 1980) refer to this reliance on anecdotal evidence as a "man-who" argument. When presented with statistics, we may refute these data with our own observations of, "I know a man who ......... ':
One reason that people misguidedly use the representativeness heuristic is because they fail to understand the concept of Lase rates -the prevalence of an event or characteristic within its population of events or characteristics. In everyday decision making, people often ignore base-rate information even though it is important to effective judgment and decision-making. In many occupations the use of base-rate information is essential for adequate job performance. Of course people use other heuristics as well.
The Availability Strategy
Most of us at least occasionally use the availability heuristic (Tversky Kahneman, 1973), in which we make judgments on the basis of how easily we can call to mind what we perceive as relevant instances of a phenomenon. For example, consider the letter R. Are there more words in English language that begin with the letter R or that have R as their third letter? Most respondents say that there are more words beginning with the letter R (Tversky & Kahneman (1973). Why? Because generating words beginning in the letter R is easier than generating words having R as the third letter. In fact, there are more English-language words with R as their third letter .
The availability heuristic has also been observed in regard to everyday situations. Michael Ross and Fiore Sicoly ( 1979) asked married partners individually to state which of the two partners performed a larger proportion qf each of 20 different household duties (e.g., grocery shopping or preparing breakfast). Each partner stated that he/she more often performed about 16 of the 20 chores. If each partner was correct, it appears that in order to accomplish 100% of the work in a household each partner must perform 80% of the work. Although clearly 80%+80%=100%. We can understand why people may engage in using the availability heuristic when it confirms their beliefs about themselves. However, people also employ the availability heuristic when its use leads to a logical fallacy that has nothing to do with their beliefs about themselves. Sometimes availability heuristic might have to the conjunction fallacy, in which an individual gives a higher estimate for a subset of events than for the larger set of events containing the given subset.
A variant of the long junction fallacy is the inclusion fallacy, in which the individual judges a greater likelihood that every member of an inclusive category (e.g., lawyers) has a particular characteristic then that every member of a subset of the inclusive category (e.g., labor-union lawyers) has that characteristic (Shafir, Osherson, & Smith, 1990).
Heuristics such as representativeness and availability do not always lead to wrong judgments or poor decisions. Indeed, we use these, mental short cuts because they are so often right. Because we generally make decisions in which the most common instances are the most relevant and valuable ones, the availability heuristic is often a convenient short cut with few costs. However, when particular instances are better recalled due to biases (e.g., your views. of your own behavior, in comparison with that of the other persons), the availability heuristic may lead to less than optimal decisions.
SUMMARY
Of the strategies used to solve problems, some are general purpose, whereas others are task-specific. Means-end analysis is a general heuristic in which the solver discerns the differences between a present state and the goal state and then takes actions that reduce those differences. This strategy is particularly effective in solving tasks that can be divided into subtasks. Although means-end analysis is the central strategy in some theories of problem solving, it is but one of many strategies and people rarely use it in a highly rigid manner. The efficiency of the problem solving depends largely on the extent to which the subject limits the size of the search space, the set of moves the solver might consider, so that only the strongest moves are examined. People limit the size of the search space by using strategies such as remembering moves that have worked in the past, reasoning by analogy, and engaging in a constructive search. People also use search strategies to collect evidence that can be used to evaluate hypotheses, as in scientific inquiry. One search method that is widely used is the confirmation strategy, in which the solver looks for evidence that could confirm a hypothesis but not for evidence that could falsify it. Although attempts at falsification are required for evaluating a hypothesis fully, the confirmation strategy is useful in the early stages of inquiry.
Strategies are also used to make probabilistic inferences. For example, people predict whether a person is likely to study computer science by evaluating how similar that person is to the prototypical students of computer science. This representativeness strategy often leads to the occurrence of errors and illusions concerning the validity of the prediction. Errors also result from the use of the availability strategy, in which people use the retrievability of an event to judge how frequently that event occurs. Overall, however, the use of stratifies helps people to solve problems, particularly those that cannot be solved algorithmically.